CAT 2022 Slot 3 · Quant · Question 4

After the first transfer the glass holds 500-150=350 cc of milk and nothing else.

The cup holds its original 500 cc of water plus the 150 cc of milk, a total of 650 cc.

In that cup the milk fraction is \frac{150}{650}=\frac{3}{13} and the water fraction is \frac{500}{650}=\frac{10}{13}.

The second transfer sends 150 cc of this mixture back to the glass.

That carries 150\times \frac{3}{13}=\frac{450}{13} cc of milk and 150\times \frac{10}{13}=\frac{1500}{13} cc of water.

So the water now sitting in the glass is \frac{1500}{13} cc.

The milk left in the cup is 150-\frac{450}{13}=\frac{1950-450}{13}=\frac{1500}{13} cc.

The two quantities are identical, so the ratio is 1:1 — the third option.

Shortcut. Both containers end up holding exactly 500 cc again, since equal volumes went each way. Whatever water has left the cup must have been replaced by milk, so the water in the glass and the milk in the cup are always equal — the ratio is 1:1 regardless of the numbers.